Multi-way loudspeakers that use two or more drive units to convey a range of audio frequencies require filters at the crossover points to ensure a well formed magnitude response. However, these filters may combine to introduce a raised group delay on certain frequencies which may cause a smearing of the perceived sound.
Several methods are known that avoid uneven group delay through a crossover, including the use of first-order crossover responses or those derived using a subtractive method [Small, R. H., “Constant Voltage Crossover Design”, Proc IREE Australia, Vol 31 No 3, 1970 March, pp. 66-73], the use of a filler-driver [Baekgaard, E, “A Novel Approach to Linear Phase Lousdpeakers using Passive Crossover Networks”, J. Audio Eng. Soc, Vol 25, No 5, pp 284-294] and linear-phase crossovers normally derived using digital signal processing (DSP).
Methods are also known for smoothing the group delay introduced by a crossover system by applying a complementary all-pass correction [Linkwitz, S. H., “Active Crossover Networks for Non-Coincident Drivers”, J. Audio Eng Soc, Vol 24 No 1/2, 1976 January/February, pp. 2-8].
An acoustic transducer normally has a natural low-frequency cut off and the combination of a transducing element on a baffle or in an enclosure exhibits a high-pass frequency response which may be modelled as a high-pass filter system. This high-pass response can present significant or uneven group delay. The increase in low frequency group delay near system cut-off may be of the order of the period of the cut-off frequency. If left uncorrected, a listener can observe the low frequency components of a composite sound signal arriving after their higher frequency counterparts.
According to the overall design of the transducer and enclosure, the low-frequency response can exhibit slower-roll off (in an over-damped system), a second-order high-pass response in a closed-box system, a fourth-order high-pass in a system incorporating a vent, auxiliary radiating element or coupled cavity, or any of these in conjunction with an additional auxiliary filter which preconditions the audio so as to provide low-frequency extension, optimise alignment, or introduce intermediate or higher-order high-pass responses. In general, systems will exhibit a raised group delay at some low frequencies as a result of the overall system design and that delay bump will tend to be lower in proportion to the order of the overall system acoustic response. For this reason, for certain high-quality applications closed-box loudspeakers have hitherto been preferred over vented or higher-order designs.
The high-pass response of a loudspeaker system can be modelled as a filter which may in turn be factored into a cascade of first and second-order elements, some of which will relate to the mechanical properties of the transducer in its enclosure and others to pre-processing of the signal. It is also known that a higher-order response, such as sixth-order Butterworth, can be designed in four ways which combine pairs of its second-order factors to synthesise the mechanical system, while the third can be an auxiliary filter; normally the combinations are selected to provide the smallest enclosure volume. [Thiele, A. N. (1973). “Loudspeakers, Enclosures and Equalisers,” Proc. IREE, 34(11), pp. 425-448.]
Non-real-time methods are known, whereby audio can be pre-processed in reverse time through an all-pass filter having the same phase response as the total system; this audio when later reproduced results in a uniform group delay response. However, it is not always convenient to pre-process the audio and particularly is inconvenient to do so for different designs.
It is not possible to use a real-time causal stable filter to impart a negative delay to compensate for unwanted group delay. However, an all-pass filter which has a flat magnitude response may be used to add group delay at a specific range of frequencies. A method that adds a series of all-pass filters to carry out limited equalisation is described in M. F. Quélhas, A. Petraglia, and M. R. Petraglia, “Efficient group delay equalization of discrete-time IIR filters”, European Signal Processing Conference, pp. 125-127, 2004. However, this approach alone does not provide sufficient means for equalising the group delay of the entire multi-way loudspeaker.
In real-time, to obtain a uniform group delay it is necessary to delay the entire audio so that no part arrives earlier than the latest component arriving from the overall system; that maximum group delay is normally associated with the system low-frequency high-pass response and may be several tens of milliseconds.
In principle, an all-pass filter can be designed to correct for a high-pass response. However, to cover the frequency range from below 100 Hz to above 20 kHz would require a very large number of filters (of the order of five hundred second order all-pass filters evenly spaced across the required frequency range) and risk the accumulation of considerable noise.
Real-time techniques involving reverse block processing of a signal have also been described that do provide an opportunity for equalising the group delay, such as in Adam, V. and Benz, S., “Correction of crossover phase distortion using reversed time all-pass IIR filter”, Audio Engineering Society, 122nd Convention, Paper 7111, 6 pp., 2007. However, for precise high-sample-rate systems these approaches require very large buffers to ensure that filter states converge at the block or buffer boundaries. This method also imposes a significant start-up delay on the audio whilst adequate buffers are filled and such delay may for example be incompatible with associated video.
As will be appreciated from the above discussion, there is a need for a practical method for implementing group delay equalisation of multi-way loudspeakers with low additional latency.